import java.lang.Math;
/*
 * author: @AKS1996
 * Guass Legendre Algorithm
 * ref https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm
 *
 */

public class GuassLegendre {

	public static void main(String[] args) {
		for(int i=1;i<=3;++i)
			System.out.println(pi(i));

	}

	static double pi(int l){
		/*
		 * l: No of loops to run
		 */

		double a = 1,b=Math.pow(2,-0.5),t=0.25,p=1;
		for(int i=0;i<l;++i){
			double temp[] = update(a,b,t,p);
			a = temp[0];
			b = temp[1];
			t = temp[2];
			p = temp[3];
		}

		return Math.pow(a+b, 2)/(4*t);
	}

	static double[] update(double a, double b, double t, double p){
		double values[] = new double[4];
		values[0] = (a+b)/2;
		values[1] = Math.sqrt(a*b);
		values[2] = t - p*Math.pow(a - values[0],2);
		values[3] = 2*p;

		return values;
	}

}
